The isoperimetric inequality in steady Ricci solitons
Differential Geometry
2019-12-12 v1
Abstract
We prove that the isoperimetric inequality is satisfied in the cigar steady soliton and in the Bryant steady soliton. Since both of them are Riemannian manifolds with warped product metric, we utilize the result of Guan-Li-Wang to get our conclusion. For the sake of the soliton structure, we believe that the geometric restrictions for manifolds in which the isoperimetric inequality holds are naturally satisfied for steady Ricci solitons.
Keywords
Cite
@article{arxiv.1912.05250,
title = {The isoperimetric inequality in steady Ricci solitons},
author = {Yuqiao Li},
journal= {arXiv preprint arXiv:1912.05250},
year = {2019}
}
Comments
6 pages